newtonian mechanics - Buoyant force when object is between two liquids

Suppose we have a ball floating in liquid A. Then we pour a liquid B on top of the ball (Assuming that the liquid is poured such that the ball doesn't oscillate) . The ball rises up. Why? According to me, the liquid on top (liquid B) will exert a force downward on the ball and it should go lower. The particles in the liquid B will exert an normal force which is acting downwards on the ball. How can adding liquid B make it rise up, that is, provide an upward force?

Taking a specific case, density of B > density of ball > density of A what would happen?

Answer

There's a key factor you're missing when you're considering the added weight on the ball.

The fluid B wont just be pushing down on the top of the object floating in liquid A, it also pushes down on liquid A itself. Due to the hydrostatic principle, this therefore increases the pressure of liquid A. This added pressure increases the force that liquid A is exerting on the object in the upwards direction. This is already enough to cancel out the effects of the added weight on top of the object.

As far as the additional height goes, this is because fluid B is more dense than air. Using Archimedes' principle, we can see that this should necessarily increase the buoyant force on the object because $$F_{Buoyant} = \rho_{fluid} V g$$ (where V is volume displaced by the submerged object, $\rho_{fluid}$ is the density of the fluid and $g$ is acceleration due to gravity.

We can see that when the density of the surrounding fluid increases (and it should be safe to assume fluid B is more dense than the air formerly above fluid A), the buoyant force increases, which will result in more lift on the submerged object. As it rises, the effective density of the fluid will decrease, as more and more of the object gets surrounded by the less dense fluid B, instead of fluid A. (Buoyancy then becomes $F_{buoyant} = ( \rho_{A} V_{A} + \rho_{B} V_{B} ) g$ where $V_A$ and $V_B$ are the volumes that each fluid acts on respectively) If fluid B is more dense than the object, it will continue to rise until it floats on fluid B; if fluid B is less dense than the object, it will rise until $F_{buoyant} = F_{gravity}$ and it reaches an equilibrium position between the two fluids.